钻柱内声传输特性的信道建模与分析

Modeling and Analysis of Acoustic Transmission Characteristics in Drillstring

为准确获取钻柱信道内声信号传输特性,基于一维低频纵波传输理论,应用有限差分法和传递矩阵法构建了周期性管结构钻柱信道模型,引入不同接收边界、钻柱长度等实际条件进行了信道瞬态响应仿真,研究了两种建模方法在信道模型求解中的性能,并分析了空间步长对信道模型分析的影响规律。计算结果表明,两种方法均能获得通阻带交替且通带伴有谐振尖峰的梳状滤波器频谱结构;但对于较长钻柱,受网格划分与步长选取影响,有限差分法引入的数值计算误差将产生频散,并导致通带平滑且谐振尖峰数目减少,而传递矩阵法则更适用于较长或具有非周期性结构的复杂钻柱信道频域分析。

By using the finite difference method and transfer matrix method,the acoustic transmission models in the periodic cascade channel are respectively established to accurately achieve acoustic transmission characteristics in drillstring.The presented models are on the ground of the one-dimensional low-frequency extensional wave transmission theory.By introducing the actual channel boundaries including the conditions of receiving end and the length of drillstring,the transient responses of drillstring channel are studied by simulation to analyze synthetically the performance of solving channel models in relation to the two above-mentioned modeling methods.In this case,the effects of space-step on channel model analysis are also illustrated.The numerical simulation results show that both the two modeling methods can determine analytically the characteristic of the frequency distribution like bandpass filter and fine structure in the passbands with its number related to the number of joints.However,for the finite difference method,the numerical computation errors caused by improper finite element meshes and space-steps will result in numerical dispersions which produce the phenomena of smoother frequency responses and less fine structure patterns in the passbands.Especially for a longer drillstring,the phenomena will become more obvious.As a result,it's more preferable that the transfer matrix method is used for the channel modeling and analysis in frequency domain for a much longer or non-periodic complicated drillstring.